Quantization noise is a type of noise that results from error in the conversion of an analog signal to a digital form by an analog-to-digital converter (ADC). Digital signals have discrete steps in amplitude, while analog signals can be smooth. So while an analog signal may rise or fall like a ramp, a digital signal rises or falls in discrete steps, like a staircase. When a smooth analog signal is transformed into a signal with steps, a certain amount of error results because portions of the analog signal between the steps must be converted to a signal that skips from one step to another rather than smoothly varying between them. This makes a smooth analog signal look like a noisy analog signal. To eliminate this type of additional noise, designers try to use ADCs with a lot of steps; the more steps, the finer the graininess caused by jumping between steps. However, there are practical reasons for using the ADC with the smallest number of steps possible. One is that using more steps can make the downstream equipment that uses the digital signal very expensive because each signal level must be encoded by a large amount of data.
The design of signal conditioning systems involving the conversion of analog signals to digital form invariably confronts the issue of quantization noise, although in most cases, it is just a routine step in the design process. But in some kinds of signal analysis systems, such as Magnetic Resonance Imaging (MRI), quantization noise is not so easily addressed. This is because of a characteristic of certain signals known as “dynamic range,” which refers to how much variation the signal exhibits in its amplitude. A signal with a large dynamic range contains useful data at portions that are high in amplitude and at portions that are low in amplitude. In MRI systems, this problem is acute because useful information is contained in the signal all the way down to the point at which its amplitude approaches zero. The problem with handling such signals arises because of the large number of ADC steps required when a signal varies greatly in amplitude. Ideally, the designer wants as many steps as possible to minimize the quantization noise. However, the amount of noise in the original analog signal places a lower limit on how much a greater number of steps will ultimately increase the quality of the digital signal. It makes no sense to add more steps to the ADC when the steps of the ADC are already much smaller than noise in the original analog signal. Trying to reduce the magnitude of a very small quantization noise added to a signal that already has a much higher noise level, is wasteful because it takes a lot of computing power to handle a digital signal with a lot of amplitude steps. Therefore, the best approach is to select an ADC whose step size (least significant bit) is smaller than the amplitude of the noise part of the original analog signal.
The problem addressed by the invention occurs when the size of the noise part of the signal is so much smaller than the peak signal that a tremendous number of steps are required in the ADC to insure the noise part of the signal is smaller than the step size. This type of analog signal, one where the noise level is much lower than the signal's peak, is called a signal with large dynamic range.
In MRI, a receiving coil measures magnetic resonance properties of a sample of material under study (e.g., a patient's body). The receiving coil outputs a resonance signal that varies greatly in amplitude in very short bursts. To obtain this signal, the sample has to be subjected to various cycles of magnetic fields and a burst of radio energy, after which, the receiving coil receives a burst of return radio energy. This is repeated many times for each image, each time using a slightly different magnetic field, called the phase-encoding gradient. The phase-encoding gradient makes each physical part of the sample radiate a slightly different signal so that a computer can determine the correspondence between a portion of the signal and the physical part of the sample.
Each of the signal bursts of return radio energy corresponds to a unique cycle corresponding to a different phase encoding gradient. These signals are stored in a matrix, with the corresponding phase encoding varying by row and time (from beginning to the end of the signal) varying by column. Then some mathematics is performed on the rows and columns to transform the rows and columns of signal data to rows and columns of an image, like the pixels of a computer monitor. To do the mathematics requires that all the signals be stored as numbers and that is where the ADC comes in.
The amplitude for each signal corresponding to a given phase encoding level can vary over a very wide range. However, that range normally varies from one phase encoding level to the next; the range tends to swell and then taper off as the phase-encoding level is varied. The signal range also varies with slice thickness, pulse repetition time, echo time, sample material size, sample material fat content, the type of receiver coil, etc., but these remain constant during a given imaging sequence. The prior art method of dealing with the range of the signal is to do a calibration procedure to determine the highest signal level likely to be encountered during the imaging sequence. Then the gain of the amplifier is set to the highest level that prevents the peak signal level from exceeding the upper limit of the ADC (called, “over-ranging”) thereby squeezing as many ADC steps as possible within the amplitude range of the signal. Despite this, since the resonance signal can range over multiple orders of magnitude in a single imaging sequence, the amplification is such that the noise amplitude is still smaller than a step size, unless very expensive ADCs are used. There is also a tradeoff between resolution and speed of the ADC and price reflects this.
Another prior art approach has been to vary the gain during an imaging sequence. The gain is varied so that a low gain is used at times during which the signal amplitude is high and the high gain is used at times during which the signal amplitude is low. In principle, this insures that the quantization noise figure remains independent of the gain.
In practice, the prior art techniques applied heretofore have suffered from other sources of error and/or undue capital and operating costs, particularly in regard to the resonance signal analog processing. In U.S. Pat. No. 5,023,552, for example, the raw resonance signal from the receiving coil is applied to a variable gain amplifier to adjust the gain between successive resonance signal acquisitions so that the ADC is driven to substantially full output. The amplified resonance signal is then down-converted (a step in which a non-information-bearing part of the raw signal is filtered out of an information-bearing part) before being applied to the ADC. The digital signal is then mathematically processed to generate images. The signal's timing and amplitude are altered by these steps—called phase and gain error—and are compensated digitally, either before or after N-dimensional Fourier transform of the baseband signal. A calibration process is used to determine the settings of the analog amplifier and the compensation required to correct the phase and gain error. But this solution to the dynamic range problem has drawbacks. In prior art systems, the signal is amplified and down-converted before being applied to an ADC. Analog amplification and down-conversion at such high frequencies makes the analog hardware particularly sensitive to introducing gain and phase error. The errors must be accurately compensated by calibration. The calibration step, in which a known signal is applied to the receiver coil, must therefore be performed carefully and precisely to generate a lookup table for accurate compensation. But even with a calibration, changing gain during operation can introduce errors that are not entirely mitigated by calibration-based compensation and even though careful design and component selection can mitigate them, the hardware costs are high. Also, temperature, time, vibration, and other factors can affect the analog components such as variable amplifiers, reference frequency generators, phase-sensitive rectifiers, etc., particularly in view of the sensitivity of the image processing to phase error and the high frequencies at which the analog front end is operating. The functional shortcomings of the analog down-conversion components place limits on the quality of images that can be produced and the increase the costs of signal processing equipment. In addition, the calibration is a time-consuming nuisance that slows amortization and adds to the life-cycle costs of MRI systems.